Question

Explain the following terms:
i. Rate constant(k)
ii. Half-life period of reaction $\left( {{t_{1/2}}} \right)$

Answer 1

Hint: Chemical kinetics deals with the study of rate of chemical reaction and factors affecting rate of reaction. To know about rate constant and half-life, we should understand the rate law expression.

Complete answer:
The rate law expression is the mathematical relationship between the concentration and the reaction rates of the reactants. It can be written as:
$Rate = \frac{{dx}}{{dt}} = k{\left[ A \right]^m}{\left[ B \right]^n}$
Where m and n are the orders of the reaction. (k) is the rate constant.

i. Rate constant (k) is defined as the rate of the reaction when the concentration of the one or more than one reacting species approaches to or equal to unity. Rate constant is also called a velocity constant and specific rate constant. The rate constant depends on the temperature but it is independent of the concentration. The temperature dependence of the rate constant can be seen by the Arrhenius equation:
\[k = A{e^{\frac{{ - {E_A}}}{{RT}}}}\]
where, \[{E_A}\] is the activation energy, \[R\]is the gas-constant and A is the frequency factor. T is the absolute temperature.

ii. The half-life period of a reaction $\left( {{t_{1/2}}} \right)$ is defined as the time required for an initial concentration of the reactant to be reduced to one-half of the initial value. It can be better explained with the help of example- if the initial concentration of the reaction is 2M and in 40 minutes the initial concentration of the reactants falls to half in 40 minutes i.e., 1M, it is called as half-life of reaction.

Note:
Remember that the rate constant unit for different orders will be different. Unit of rate constant depends on the order of the reaction. To determine the half-life, order of the reaction and rate constant needed.